Time domain equalization for discrete multi-tone systems

ABSTRACT

A multiple carrier communication system includes a primary impulse shortening filter that receives an output signal of an analog to digital converter and accepts coefficients. A secondary impulse shortening filter receives the output signal of the analog to digital converter, outputs an output signal, and passes coefficients to the primary impulse shortening filter. A reference signal generator outputs a reference signal. A comparator compares the output signal and the reference signal and outputs a resulting error signal. An adaptive processor computes coefficients for the secondary impulse shortening filter based on the error signal.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.10/320,920 filed on Dec. 17, 2002, now U.S. Pat. No. 6,785,328 whichclaims priority from U.S. application Ser. No. 09/233,914, filed Jan.21, 1999, which claims priority from U.S. Provisional Application No.60/087,336, filed May 29, 1998. The disclosures of those applicationsare incorporated herein by reference.

BACKGROUND

The invention relates to time-domain equalization in a discretemulti-tone (DMT) receiver.

Conventional single carrier modulation techniques translate data bitsfor transmission through a communication channel by varying theamplitude and/or phase of a single sinusoidal carrier. By contrast, DMT,which is also referred to as Orthogonal Frequency Division Multiplexing(OFDM) or Multicarrier Modulation (MCM), employs a large number ofsinusoidal subcarriers, e.g., 128 or 256 subcarriers. The availablebandwidth of the communication channel is divided into subchannels andeach subchannel communicates a part of the data. A DMT system may employquadrature amplitude modulation (QAM) for each of the subcarriers.

OFDM-based systems transmit blocks of information bits. The timerequired to transmit one such block is called the symbol period. Thetime domain waveform that corresponds to one such block of bits iscalled a symbol.

Intersymbol interference (ISI) arises from the characteristics ofpractical communication channels and limits the rate at whichinformation can be transmitted through them. Specifically, communicationchannels typically have an Effective Discrete-Time Impulse Response(EDIR) that is greater than one sample time in length, which causes ISI.ISI is a well-known phenomenon in single-carrier communication systemsand there are many techniques for reducing it. The process of such ISIreduction is called equalization. ISI is discussed, for example, inProakis, Digital Communications, McGraw Hill, 2nd Edition, 1989.

Equalization in OFDM-based systems is achieved by a two stage process.First, at the transmitter, a Cyclic Prefix (CP) is employed by affixingan end-portion of each symbol to the beginning of the symbol. A cyclicprefix that is greater than the EDIR of the channel prevents one symbolfrom interfering with another. Furthermore, it also facilitates a simplemethod of neutralizing the time domain spread of each symbol forced bythe channel. This is achieved through a simple frequency domain processin the receiver which requires one multiplication operation for eachsubcarrier used. The use of a Cyclic Prefix to reduce ISI is discussed,for example, in: Cimini, “Analysis and Simulation of a Digital MobileChannel using Orthogonal Frequency Division Multiplexing,” IEEETransactions on communications, pp 665-675, July 1985; Chow, “A DiscreteMulti-Tone Transceiver System for HDSL applications,” IEEE Journal onSelected Areas of Communications, 9(6):895-908, August 1991; and “DMTGroup VDSL PMD Draft Standard Proposal,” Technical Report,T1E1.4/96-329R2, ANSI 1997.

Another problem arising in conventional DMT systems is noise bleeding,which occurs when noise from one frequency band interferes with a signalwhose subcarrier is in another frequency band. Noise bleeding is caused,in general, by a discrete Fourier transform (DFT) operation at thereceiver. Noise bleeding is discussed in, for example, Worthen et. al.,“Simulation of VDSL Test Loops,” Technical Report T1E1.4/97-288, ANSI1997.

In a perfectly synchronized DMT system, a signal in one frequency banddoes not interfere with a signal whose subcarrier is in anotherfrequency band. However, noise from one band may interfere with otherless noisy bands and render them unusable. Techniques for dealing withnoise-bleeding include wavelet-based solutions. However, wavelet-basedsolutions are, in general, computationally intensive.

Other references dealing with time domain equalization include: Chow, J.S. and Cioffi, J. M., “A Cost-effective Maximum Likelihood Receiver forMulticarrier Systems”, Proceedings of the ICC, 1992; Melsa, Peter J. W.,Younce, Richard C., and Rohrs, Charles E., “Optimal Impulse ResponseShortening”, Proceedings of the thirty-third Annual Allerton Conferenceon Communication, Control and Computing, 1995, pp. 431-438; Harikumar,Gopal and Marchok, Daniel, “Shortening the Channel Impulse Response ofVDSL Loops for Multicarrier Applications”, Technical reportT1E1.4/97-289, ANSI, 1997.

SUMMARY

A spectrally constrained impulse shortening filter (SCISF) may be used,for example, in DMT systems. The coefficients of the SCISF may becomputed efficiently. For example, the coefficients may be computed andchanged through a training process that may occur upon start up of thecommunication system and periodically during its operation.

The SCISF serves two primary functions. First, it reduces intersymbolinterference (ISI) by reducing the length of the effective discrete-timeimpulse response (EDIR) of the communication channel. Conventionalimpulse shortening filters may have deep nulls in their frequencyresponse. By contrast, the SCISF has a filter characteristic that isessentially free from undesired nulls that may attenuate or completelyeliminate certain subcarriers.

Second, the SCISF reduces noise bleeding between subcharnels byattenuating noisy channels in a manner that does not reduce the signalto noise ratio (SNR) in these channels, but reduces the noise power thatmay appear in the sidelobes of adjacent subchannels. The SCISFaccomplishes these functions by applying a frequency constraint to thesignal based on a desired spectral response.

The coefficients of the SCISF are computed independent of the length ofthe cyclic prefix, the symbol length, and the frequency domainequalization characteristics of the system. The SCISF is particularlyeffective in systems in which additive noise dominates intersymbolinterference, or in which noise bleeding predominates. The SCISF reducesnoise bleeding with a filter structure that is shorter than thatobtained with other techniques. Consequently, the SCISF is less complexand its coefficients are easier to compute, which reduces systemcomplexity and cost. The SCISF may be particularly well suited, forexample, for very high-speed digital subscriber lines (VDSL) systems,which generally have low intersymbol interference and tend to sufferfrom noise bleeding.

In addition, dynamic selection of a cyclic prefix (CP) that maximizesthe data throughput for a communication channel having a particularnoise profile is provided. Dynamic selection of the CP allows thecommunication system to adapt to changing noise conditions in thecommunication channel.

In one aspect, generally, a primary impulse shortening filter is adaptedin a multiple carrier communication system. A secondary impulseshortening filter is provided. An output signal of the secondary impulseshortening filter is compared to a reference signal to compute an errorsignal. Coefficients of the secondary impulse shortening filter arecomputed in an adaptive processor based on the error signal.Coefficients of the primary impulse shortening filter are replaced withcoefficients of the secondary impulse shortening filter.

Embodiments may include one or more of the following features. An outputsignal of the primary impulse shortening filter may be decoded to formoutput data. The output data may be encoded to form the referencesignal. A discrete Fourier transform may be applied to the output signalof the primary impulse shortening filterprior to decoding the outputsignal. An inverse discrete Fourier transform may be applied to theencoded output data in forming the reference signal.

A digital signal may be received from an output of an analog to digitalconverter. The digital signal may be input to the primary impulseshortening filter. The digital signal may be delayed. The delayeddigital signal may be input to the secondary impulse shortening filterand the adaptive processor.

The encoded output data may be scaled with a set of scaling factors informing the reference signal. The scaling factors may be determined by:measuring received noise power spectral density, computing a desiredspectral response based on the measured noise power, and computing thescaling factors so that the coefficients computed in the adaptiveprocessor provide the secondary impulse shortening filter with aspectral response that matches the desired spectral response. A discreteFourier transform may be applied to the output signal of the primaryimpulse shortening filter prior to decoding the output signal. The noisepower spectral density may be measured at an output of the discreteFourier transform. An inverse discrete Fourier transform may be appliedto the scaled, encoded output data.

In another aspect, an impulse shortening filter is adapted in a multiplecarrier communication system having a spectrally constrained impulseshortening filter. An output signal of the spectrally constrainedimpulse shortening filter is compared to a reference signal to computean error signal. Coefficients of the spectrally constrained impulseshortening filter are computed in an adaptive processor based on theerror signal.

Embodiments may include one or more of the following features. Thereference signal may be a predetermined signal stored in a memory in thecommunication system. A discrete Fourier transform may be applied topredetermined reference values to form transformed reference values. Thetransformed reference values may be scaled with a set of scaling factorsto form scaled. An inverse discrete Fourier transform may be applied tothe scaled values to form the reference signal.

A data signal may be received from an output of an analog to digitalconverter. The data signal may be input to the spectrally constrainedimpulse shortening filter and the adaptive processor.

In another aspect, a multiple carrier communication system includes aprimary impulse shortening filter that receives an output signal of ananalog to digital converter and accepts coefficients. A secondaryimpulse shortening filter receives the output signal of the analog todigital converter, outputs an output signal, and passes coefficients tothe primary impulse shortening filter. A reference signal generatoroutputs a reference signal. A comparator compares the output signal andthe reference signal and outputs a resulting error signal. An adaptiveprocessor computes coefficients for the secondary impulse shorteningfilter based on the error signal.

Embodiments may include one or more of the following features. Adiscrete Fourier transform may receive an output signal of the primaryimpulse shortening filter. A decoder may receive the transformed outputsignal from the discrete Fourier transform. The reference signalgenerator may include an encoder that receives output data from thedecoder. The reference signal generator may include a scaling filterthat scales the output data from the encoder using a set of scalingfactors. An inverse discrete Fourier transform may receive the scaledoutput signal from the scaling filer.

In another aspect, a multiple carrier communication system may include aspectrally constrained impulse shortening filter that receives an outputsignal of an analog to digital converter and accepts coefficients. Areference signal generator outputs a reference signal. A comparatorcompares the output signal and the reference signal and outputs aresulting error signal. An adaptive processor computes coefficients forthe spectrally constrained impulse shortening filter based on the errorsignal.

Embodiments may include one or more of the following features. A memorymay store the reference signal as a predetermined signal. A discreteFourier transform may receive the reference signal from the memory. Ascaling filter may scale the reference signal using a set of scalingfactors. An inverse discrete Fourier transform may receive the scaledreference signal.

Other features and advantages will be apparent from the followingdetailed description, including the drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a discrete multi-tone communication systemwith a spectrally constrained impulse shortening filter.

FIG. 2 is a block diagram of a system for adapting a spectrallyconstrained impulse shortening filter in an initial training process.

FIGS. 3A and 3B are block diagrams of a system for adapting a spectrallyconstrained impulse shortening filter in an periodic or continuoustraining process.

FIG. 4 is a block diagram of a generalized adaptation system thatemploys frequency scaling in the feedback loop.

FIG. 5 is a block diagram of a system for adapting a spectrallyconstrained impulse shortening filter in an initial training processthat includes frequency scaling in the feedback loop.

FIGS. 6A and 6B are block diagrams of a system for adapting a spectrallyconstrained impulse shortening filter in an periodic or continuoustraining process that includes frequency scaling in the feedback loop.

FIGS. 7A-7D are plots of simulation results for a discrete multi-tonesystem.

FIGS. 8A-8D are plots of simulation results for a discrete multi-tonesystem.

DESCRIPTION

As shown in FIG. 1, a discrete multi-tone (DMT) communication system 10has a transmitter 12 and a receiver 14. The transmitter 12 accepts aninput data bit stream which passes through a constellation encoder 20.The encoder 20 divides the serial input bit stream into blocks of data.These blocks of data are further subdivided into smaller blockscorresponding to subchannels. Each of these smaller blocks are used tocompute a complex value representing a constellation point. Eachconstellation point corresponds to a subsymbol. The subsymbols are thenoutput by the encoder. Taken together, the subsymbols constitute asymbol.

The subsymbols are supplied to an inverse discrete Fourier transform(IDFT) 30, which may be implemented, for example, in a digital signalprocessor. The IDFT 30 outputs N time samples of a symbol. The timesamples are processed by a parallel to serial converter 40 to form asingle stream of time samples.

Following the parallel to serial converter 40, a prefix adder 50 adds acyclic prefix to the beginning of each symbol to reduce intersymbolinterference (ISI). Alternatively, the cyclic prefix may be added in theparallel to serial converter. After the cyclic prefix is added, theresulting signal passes through a digital-to-analog (D/A) converter 60for transmission to the receiver 14 through a communication channel 70.An analog transmit filter 65 may be included following the D/A converterto band limit the transmitted signal.

At the receiver 14, the signal passes through an analog-to-digital (A/D)converter 80 and then through a spectrally constrained impulseshortening filter (SCISF) 90. A prefix stripper 100 strips the cyclicprefixes from the resulting symbols and a serial to parallel converter110 divides the stream of time samples into parallel signal paths thatform the inputs to a discrete Fourier transform (DFT) 120. The DFT 120converts the time samples into subsymbols. A frequency domainequalization filter 130 equalizes the subsymbols. A decoder 140 convertsthe subsymbols into a data bits and outputs the resulting data. Ananalog receive filter 75 may be included prior to the A/D converter inorder to band limit the received signal.

As discussed above, a cyclic prefix is added to each symbol prior totransmission through the communication channel to reduce the effects ofISI. The cyclic prefix is added by copying the last v time samples fromthe end of a symbol and placing them at the beginning of the symbol. Toeliminate ISI, the length of the cyclic prefix, v, is chosen to belonger than the effective discrete-time impulse response (EDIR) of thechannel. However, because the cyclic prefix constitutes redundant data,increasing the length of the cyclic prefix reduces the efficiency of thecommunication system. For example, in a system having N time samples persymbol and a cyclic prefix of v time samples, the efficiency of thesystem will be reduced by a factor of N/(N+v). Efficiency may bemaximized either by minimizing v or maximizing N. However, increasing Nincreases the complexity, latency and computational requirements of thesystem and at some point becomes impractical. Accordingly, it isdesirable to minimize v.

A spectrally constrained impulse shortening filter having an impulseresponse, g(n), may be employed in the receiver to minimize the lengthof the cyclic prefix by decreasing the EDIR of the effectivecommunication channel, which includes the transmit and receive filters,the impulse shortening filter, and the physical transmission channel.The use of an impulse shortening filter is referred to as time domainequalization. Decreasing the EDIR allows a shorter cyclic prefix to beused without increasing ISI.

The SCISF may be configured, by determining the filter-coefficientsduring a training or adaptation period. The SCISF filters the output{y_(k)} of the receiver A/D 80. The coefficients are selected using analgorithm that minimizes the squared error between a reference sequence{u_(k)} generated by the receiver and the output of the SCISF {û_(k)}.The SCISF may be a finite impulse response (FIR) filter or an infiniteimpulse response (IIR) filter. The SCISF may be trained followingactivation of the communication system or periodically during operationof the system to compensate for variations in the channel noise profile.

The training may be performed using a variation of one of the classicaladaptive algorithms, such as least mean squares (LMS), normalized LMS,or recursive least squares (RLS). For example, the following algorithmis a version of the normalized LMS algorithm in which b₀, . . . , b_(N)and a₁, . . . , a_(N) are the FIR and IIR parts of a SCISF having animpulse response, g. The z-transform G(z) is:

$\begin{matrix}{{G(z)} = \frac{b_{0} + {b_{1}z^{- 1}} + \cdots + {b_{N}z^{- N}}}{1 - {a_{1}z^{- 1}} - \cdots - {a_{N}z^{- N}}}} & (1)\end{matrix}$The adaptation of coefficients a_(i) and b_(i) is defined in thefollowing equations, in which a_(i)(k) and b_(i)(k) are the values ofthese coefficients during the k^(th) iteration. The parameter μ is apredetermined constant with a value of 0.4.

$\begin{matrix}{{\hat{u}}_{k} = {{\sum\limits_{i = 0}^{N}\;{{b_{i}(k)}y_{k - i}}} + {\sum\limits_{j = 1}^{N}\;{{a_{i}(k)}{\hat{u}}_{k - i}}}}} & \left( {2a} \right) \\{\alpha_{k} = \left\lbrack {{b_{0}(k)},\ldots\mspace{11mu},{b_{N}(k)}} \right\rbrack} & \left( {2b} \right) \\{\beta_{k} = \left\lbrack {{a_{1}(k)},\ldots\mspace{11mu},{a_{N}(k)}} \right\rbrack} & \left( {2c} \right) \\{d_{k} = \left\lbrack {y_{k},y_{k - 1},\ldots\mspace{11mu},y_{k - N}} \right\rbrack} & \left( {2d} \right) \\{c_{k} = \left\lbrack {{\hat{u}}_{k - 1},{\hat{u}}_{k - 2},\ldots\mspace{11mu},{\hat{u}}_{k - N}} \right\rbrack} & \left( {2e} \right) \\{e_{k}\overset{\Delta}{=}{u_{k} - {\hat{u}}_{k}}} & \left( {2f} \right) \\{\alpha_{k + 1} = {\alpha_{k} + {\mu\frac{e_{k}d_{k}}{{d_{k}}^{2}}}}} & \left( {2g} \right) \\{\beta_{k + 1} = {\beta_{k} + {\mu\frac{e_{k}c_{k}}{{c_{k}}^{2}}}}} & \left( {2h} \right)\end{matrix}$

In a first embodiment, the coefficients of the SCISF are determinedduring an initial training period following the activation of thecommunication system using the LMS algorithm described above. Apredetermined sequence of bits x_(k) is input to the transmitter 12. Thesequence of bits results in a sequence of real numbers {x_(k)} at theinput of the D/A 60. As shown in FIGS. 1 and 2, the transmitted signalis filtered and noise-corrupted by the transmission channel 70,resulting in a received sequence {y_(k)} at the output of the A/D 80 inthe receiver 14. The SCISF 90 filters and transforms the receivedsequence {y_(k)} into an output sequence {{circumflex over (x)}_(k)}.The output sequence {{circumflex over (x)}_(k)} is compared (in a signalcomparator 205) to the predetermined sequence x_(k), which is stored inmemory 210 in the receiver. The comparison results in an error signale_(k) that is input to the LMS algorithm processor 215 along withsequence {{circumflex over (x)}_(k)}.

The training process determines coefficients for the SCISF so that theoutput {{circumflex over (x)}_(k)} matches the predetermined sequence{x_(k)} as closely as possible in a least squares sense, i.e., the meansquare error between the output and the predetermined sequence isminimized. During the training process, the coefficients of the SCISFconverge to values that enable the SCISF to reduce ISI and additivenoise. The resulting SCISF matches P₁(ω) in the frequency domain in aleast squares sense, where:

$\begin{matrix}{{P_{1}(\omega)} = \frac{{S_{x}(\omega)}{H^{*}(\omega)}}{{{S_{x}(\omega)}{{H(\omega)}}^{2}} + {S_{\eta}(\omega)}}} & (3)\end{matrix}$In the equation above, S_(x)(ω) is the power-spectral density at theinput of the transmitter D/A 60, S_(η)(ω) is the power spectral densityof the additive noise at the output of the A/D 80, and H(ω) is thefrequency response of the effective discrete-time impulse response(EDIR) of the transmission channel 70, transmit filter 65, and receivefilter 75 measured between the input of the transmitter D/A 60 and theoutput of the receiver A/D 80.

Upon completion of the initial training of the SCISF, the SCISFcoefficients are fixed and the frequency domain equalizer (FEQ 130) ofthe receiver is trained using standard techniques for DMT receivers.Following the training of the FEQ, the SCISF can be periodically trainedor adapted during operation of the communication system. Since it is notefficient to repeatedly transmit a predetermined bit sequence duringoperation of the communication system, the periodic training processuses transmitted communication data to generate the reference and outputsequences, as described below.

During operation of the communication system, a sequence ofcommunication data bits x_(k) is input to the transmitter 12 (see FIG.1). The sequence of data bits results in a sequence of real numbers{x_(k)} at the input of the D/A 60. As shown in FIGS. 1 and 3A, thetransmitted signal is filtered and noise-corrupted by the transmissionchannel 70, resulting in a received sequence {y_(k)} at the output ofthe A/D 80 in the receiver 14. The SCISF 90 filters and transforms thereceived sequence {y_(k)} into an output sequence {{circumflex over(x)}′_(k)}.

The received sequence {y_(k)} is also input to a delay 305 and then to asecondary SCISF 300 that has the same coefficients as the primary SCISF90 following the initial training. Such a configuration allows periodictraining to be performed without disruption to the operation of thecommunication system. The secondary SCISF 300 is periodically orcontinuously trained using an algorithm similar to that used for theinitial training. The new coefficients of the secondary SCISF 300 areperiodically copied to the primary SCISF 90.

In an initial training process, the output sequence {{circumflex over(x)}_(k)} of the secondary SCISF 300 would be compared (in a signalcomparator 205) to a predetermined sequence x_(k) stored in memory.However, as discussed above, a sequence of data communication bits isused as a reference sequence for training rather than a predeterminedsequence. As such, the receiver must have a way of generating areference signal to compare to the output of the SCISF.

To compute the reference sequence, the receiver essentially duplicatesthe encoding and modulation processes of the transmitter using theoutput of the decoder 140. Because the initial training has already beenperformed, the SCISF 90 output {{circumflex over (x)}′_(k)} matches thepredetermined sequence {x_(k)} closely and ISI and additive noise areminimized. Hence, the data output of the decoder 140 closely matches thetransmitted sequence of communication data bits x_(k). The data bits areinput to an encoder 320, an IDFT 330, a parallel to serial converter340, and a prefix adder 350 similar to those in the transmitter. Theoutput sequence {x_(k)} of this chain is input to the LMS algorithmprocessor 215 and used as a reference sequence in the trainingalgorithm.

The output sequence {{circumflex over (x)}_(k)} of the secondary SCISF300 is compared (in a signal comparator 205) to the reference sequence{x_(k)}, which is output by the encoding/modulation chain (320, 330, 340and 350). As noted above, the received sequence {y_(k)} passes through adelay 305 before being input to the secondary SCISF 300. The delay 305compensates for the processing delay in the demodulation/decoding chainand the encoding/modulation chain. The comparison results in an errorsignal e_(k) that is input to the LMS algorithm processor 215. Thetraining process determines coefficients for the secondary SCISF 300 sothat the output {{circumflex over (x)}_(k)} matches the referencesequence {x_(k)} as closely as possible in a least squares sense, i.e.,the mean square error between the output and the reference sequence isminimized. Periodically, the coefficients of the secondary SCISF 300 arecopied to the primary SCISF 90.

Alternatively, as shown in FIG. 3B, the periodic training may beperformed with a single SCISF 90. In this configuration, a receivedsequence {y_(k)} is output by the A/D 80 in the receiver 14. The SCISF90 filters and transforms the received sequence {y_(k)} into an outputsequence {{circumflex over (x)}′_(k)}. The received sequence {y_(k)} isalso input to a delay 305. After the received sequence {y_(k)} passesthrough the SCISF 90, a data switch 360 is changed from position A toposition B, allowing the delayed received sequence to make a second passthrough the SCISF 90. An output switch 370 also may be opened, so thatdata is not output during the training process. In addition, the SCISFcoefficients are controlled by the LMS algorithm during the trainingprocess.

A reference sequence is computed as in the configuration of FIG. 3A. Thedata bits are input to an encoder 320, an IDFT 330, a parallel to serialconverter 340, and a prefix adder 350. The resulting reference sequence{x_(k)} is input to the LMS algorithm processor.

The output sequence {{circumflex over (x)}_(k)} of the second passthrough the SCISF 90 is compared (in signal comparator 205) to thereference sequence. As noted above, the received sequence {y_(k)} passesthrough a delay 305 before being input to the SCISF 90 for the secondpass. The delay 305 compensates for the processing delay in thedemodulation/decoding chain and the encoding/modulation chain. Thecomparison results in an error signal e_(k) that is input to the LMSalgorithm processor 215. The training process determines coefficientsfor the SCISF 90 so that the output {{circumflex over (x)}_(k)} matchesthe reference sequence {x_(k)} as closely as possible in a least squaressense, i.e., the mean square error between the output and the referencesequence is minimized. The coefficients of the SCISF 90 then are updatedto the coefficients determined in the training process.

In a second embodiment, the SCISF 90 coefficients are chosen so that thefrequency response of the SCISF matches a desired spectral responseG_(d)(ω) that seeks to minimize the effects of noise-bleeding andmaximize system bit throughput. The desired spectral response G_(d)(ω)is determined based on the signal-to-noise ratios observed in thevarious frequency bins of the DFT 120 in the receiver.

For example, an OFDM system may have M tones, N of which (m₁ throughm_(N)) are used. The system operates over a channel with analogfrequency response H_(c)(f). Referring again to FIG. 1, the analog noisepower spectral density at the input of the receiver A/D 80 is S_(η)(f).Prior to receiver A/D 80, the received analog signal may be filtered byan anti-aliasing filter (i.e., receive filter 75) having a transferfunction H_(a)(f). The effective discrete-time impulse response (EDIR)of the transmission channel of the OFDM system (including the transmitfilter 65 and receive filter 75) is h(n). The output of the A/D 80 isinput to a SCISF 90 having an impulse response g(n). G(ω) is thespectral response corresponding to g(n).

The expected signal energy μ(k) observed in frequency bin k at theoutput of the DFT 120, which has a length of NM, is:

$\begin{matrix}{{{\mu(k)} = {C_{1}D_{k}{{H\left( \frac{\pi\; k}{M} \right)}}^{2}{{G\left( \frac{\pi\; k}{M} \right)}}^{2}}};{{H(\omega)} = {{H_{c}\left( \frac{\omega}{2\;\pi\; T} \right)}{H_{a}\left( \frac{\omega}{2\pi\; T} \right)}}}} & (4)\end{matrix}$where C₁ is a constant, 1/T is the sampling frequency and D_(k) is thetransmitted power in frequency bin k. The noise power η(k) in bin k is:

$\begin{matrix}\left. {\left. {{{\eta(k)} = {{C_{2}\left\lbrack {{S_{\eta}\left( \frac{\omega}{2\pi\; T} \right)}{{G(\omega)}}^{2}} \right.}{H_{a}\left( \frac{\omega}{2\pi\; T} \right)}}}}^{2} \right\rbrack*\left\lbrack \frac{\sin^{2}\left( {M\;\omega} \right)}{\sin^{2}\left( \frac{\omega}{2} \right)} \right\rbrack} \right|_{\omega = \frac{\pi\; k^{\prime}}{M}} & (5)\end{matrix}$where C₂ is a constant and * denotes a convolution of the discreteFourier transforms. If the noise in the bands occupied by unused tonesis sufficiently attenuated by the anti-alias filter (receive filter 75),η(k) is approximately:

$\begin{matrix}{{{\eta(k)} \approx {C_{3}{\sum\limits_{l = M_{1}}^{M_{2}}\;{{S_{\eta}\left( \frac{l}{2{MT}} \right)}{{G\left( \frac{\pi\; l}{M} \right)}}^{2}{{H_{a}\left( \frac{l}{2{MT}} \right)}}^{2}\left( {{\tau\left( {k - l} \right)} + {\tau\left( {{2M} - k - 1} \right)}} \right)}}}},} & (6)\end{matrix}$where τ(n) is defined as:

$\begin{matrix}{{{\tau(n)} = {\int_{- \frac{\pi\;}{NM}}^{\frac{\pi\;}{NM}}{\left\lbrack \frac{\sin^{2}\left( {M\left( {\frac{\pi\; n}{M} - \lambda} \right)} \right)}{\sin^{2}\left( {\frac{1}{2}\left( {\frac{\pi\; n}{M} - \lambda} \right)} \right)}\  \right\rbrack{\mathbb{d}\lambda}}}},} & (7)\end{matrix}$m₁ . . . m_(N) are the used tones, and C₃ is a constant. A vector offrequency magnitudes g is defined as:

$\begin{matrix}{g\overset{\Delta}{=}{\begin{bmatrix}{{G\left( \frac{\pi\; m_{1}}{M} \right)}}^{2} \\\vdots \\{{G\left( \frac{\pi\; m_{N}}{M} \right)}}^{2}\end{bmatrix} = \begin{bmatrix}G_{1} \\\vdots \\G_{N}\end{bmatrix}}} & (8)\end{matrix}$The SNR in frequency bin

$k\mspace{14mu}{is}\mspace{14mu}\frac{r_{k}G_{k}}{s_{k}^{T}g}$for scalars r_(k) and vectors s_(k). The scalars r_(k) are defined by:

$\begin{matrix}{r_{k}\overset{\Delta}{=}{C_{1}D_{k}{{H\left( \frac{\pi\; k}{M} \right)}}^{2}}} & (9)\end{matrix}$and s_(k)(l), the lth component of s_(k) is defined by:

$\begin{matrix}{{s_{k}(l)} = {C_{3}S\;{\eta\left( \frac{l}{2{MT}} \right)}{{H_{a}\left( \frac{l}{2{MT}} \right)}}^{2}\left( {{\tau\left( {k - l} \right)} + {\tau\left( {{2M} - k - l} \right)}} \right)}} & (10)\end{matrix}$

To determine an expression for g that maximizes system bit throughput,the capacity of each frequency bin k is approximated by log(1+SNR_(k)).Accordingly, the optimal spectral profile is determined by minimizingthe cost function F, where:

$\begin{matrix}{{F(g)} = {- {\sum\limits_{k = m_{1}}^{m_{N}}{\log\left( {1 + \frac{r_{k}G_{k}}{s_{k}^{T}g}} \right)}}}} & (11)\end{matrix}$

Since G_(k)=|G(πm_(k)/M)|², the minimization of the cost function isperformed over all positive values of G_(k), as:

$\begin{matrix}{g_{opt} = {\arg\;{\min\limits_{g \in G}\mspace{14mu}{F(g)}}}} & (12)\end{matrix}$

-   -   where:        G={gεR ^(N) :∥g∥=1, G _(i)≧0,1≦i≦N}.  (13)        A variety of constrained optimization strategies may be used to        solve the above equations for g_(opt).

Once the optimal impulse response g_(opt) and desired spectral responseG_(d)(ω) (which may be expressed as G_(d)(πm_(k)/M) for a system havingM tones) have been determined, a training process is used to adapt theSCISF 90 so that its impulse response g matches the desired spectralresponse. As shown in FIG. 4, the training process may be generalized asa feedback system. A reference sequence x_(k) is input to the system.This corresponds to inputting a predetermined reference bit sequence toa transmitter. The reference sequence passes through a transmissionchannel 410 having frequency response H(f) (including the physicaltransmission channel and the transmit and receive filters). Additivenoise η_(k) from the transmission channel is represented in this generalmodel as an external input 420 to the system. The resulting signal y_(k)is input to a filter 430 having a frequency response G(f), e.g., aSCISF. The output of the filter 430 is then passed to an adaptationprocessor 440, which computes an error signal based on the feedback loop450 and adapts the filter accordingly. The adaptation processor may, forexample, use the LMS algorithm described above.

The reference sequence x_(k) is also input to the feedback loop 450,which passes the reference sequence x_(k) through a scaling filter 460with frequency characteristic Q(f). The frequency characteristic Q(f) ofthe scaling filter 460 (which may be expressed as a set of frequencydomain scaling factors Q(f) is determined so that the SCISF adapts tothe desired spectral response. The output of the scaling filter 460 isused a reference for the calculation of the error signal in theadaptation processor 440, as described above.

Using the general feedback system shown in FIG. 4, a SCISF having animpulse response g may be trained to minimize the error∥q*x−x*g*h−η*g∥². The resulting filter matches P₂(ω) in the frequencydomain in a least-squares sense, where:

$\begin{matrix}{{{P_{2}(\omega)} = \frac{{S_{x}(\omega)}H*(\omega){Q(\omega)}}{{{S_{x}(\omega)}{{H(\omega)}}^{2}} + {S_{\eta}(\omega)}}},} & (14)\end{matrix}$S_(x)(ω) is the power-spectral density at the input of the system, H(ω)is the frequency response of the effective discrete-time impulseresponse (EDIR) of the transmission channel, S_(η)(ω) is the powerspectral density of the additive noise, and Q(ω) is the spectralresponse of the scaling filter 460 having impulse response q.

The solution for g_(opt) in the equations above specifies only themagnitude of the spectral response of the SCISF. If the SCISF is a FIRfilter, a linear phase characteristic may be used. If the length of theSCISF is n_(g), the desired values of G(w) for the frequency bins ofinterest are:

$\begin{matrix}{{G_{d}\left( {\pi\;{M_{k}/M}} \right)}\underset{=}{\bigtriangleup}\sqrt{g_{opt}(k)}{{\exp\left( \frac{{- {j\pi}}\;{M_{k}\left( {n_{g} - 1} \right)}}{2M} \right)}.}} & (15)\end{matrix}$

The values Q_(k) are defined by:

$\begin{matrix}{Q_{k} = \frac{{G_{d}\left( {\pi\;{m_{k}/M}} \right)}\left( {{{S_{x}\left( {{j\pi}\;{k/M}} \right)}{{H\left( {{j\pi}\;{k/M}} \right)}}^{2}} + {S_{\eta}\left( {{j\pi}\;{k/M}} \right)}} \right)}{{S_{\eta}\left( {{j\pi}\;{k/M}} \right)}H*\left( {{j\pi}\;{k/M}} \right)}} & (16)\end{matrix}$The values of Q_(k) may be computed during an initial training periodand may be periodically updated during operation of the communicationsystem.

As shown in FIGS. 5, 6A and 6B, the general feedback training processmay be used to perform an initial training of a SCISF followed byperiodic training analogous to the process described above with respectto FIGS. 1-3. One difference between the techniques is that a scaledreference signal (x*q)_(k) is used rather than an unscaled referencex_(k).

Referring to FIG. 5, to perform the initial training, a predeterminedsequence of bits x_(k) is input to the transmitter. The transmittedsignal is filtered and noise-corrupted by the transmission channel,resulting in a received sequence {y_(k)} at the output of the A/D 80 inthe receiver. The SCISF 90 filters and transforms the received sequence{y_(k)} into an output sequence {{circumflex over (x)}_(k)}. The outputsequence {{circumflex over (x)}_(k)} is compared (in a signal comparator205) to a scaled reference sequence (x*q)_(k).

The scaled reference sequence is computed from a copy of thepredetermined sequence x_(k) that is stored in memory 210 in thereceiver. As a first step, the predetermined sequence is input to aserial to parallel converter 510 and a DFT 515. The resulting frequencydomain signal is input to a scaling filter 520 which applies the set offrequency domain scaling factors Q_(k) that causes the SCISF to adapt tothe desired spectral response, as discussed above. The scaled signal isinput to an inverse discrete Fourier transform 330, a parallel to serialconverter 340 and a cyclic prefix adder 350, resulting in a scaledreference sequence (x*q)_(k). The comparison of the output sequence{{circumflex over (x)}_(k)} to the scaled reference sequence (x*q)_(k)results in an error signal e_(k) that is input to the LMS algorithmprocessor 215 along with sequence {{circumflex over (x)}_(k)}.Alternatively, a frequency domain reference (e.g., a predetermined bitsequence that has been processed by a serial to parallel converter andDFT) may be stored in memory in the receiver, which would eliminate theneed for the serial to parallel converter and discrete Fourier transformin the feedback loop.

Following the initial training, the SCISF is periodically trained duringoperation of the communication system. A sequence of communication databits x_(k) is input to the transmitter. Referring to FIG. 6A, thetransmitted signal is filtered and noise-corrupted by the transmissionchannel, resulting in a received sequence {y_(k)} at the output of theA/D 80 in the receiver. The SCISF 90 filters and transforms the receivedsequence {y_(k)} into an output sequence {{circumflex over (x)}′_(k)}.

The received sequence {y_(k)} is also input to a delay 305 and then to asecondary SCISF 300 that has the same coefficients as the primary SCISF90 following the initial training. The secondary SCISF 300 providesoutput sequence {ŷ_(k)}, which is compared to a reference sequenceduring the periodic training process. Such a configuration allowsperiodic training to be performed without disruption to the operation ofthe communication system. The secondary SCISF 300 is periodically orcontinuously trained using an algorithm similar to that used for theinitial training. The new coefficients of the secondary SCISF 300 areperiodically copied to the primary SCISF 90.

To compute the reference sequence, the data output of the decoder 140 isinput to an encoder 320. The resulting frequency domain signal is inputto a scaling filter 520 which applies the set of frequency domainscaling factors Q_(k) that causes the SCISF to adapt to the desiredspectral response, as discussed above. The scaled signal is input to aninverse discrete Fourier transform 330, a parallel to serial converter340 and a cyclic prefix adder 350, resulting in a scaled referencesequence (x*q)_(k). The comparison of the output sequence {{circumflexover (x)}_(k)} to the scaled reference sequence (x*q)_(k) results in anerror signal e_(k) that is input to the LMS algorithm processor 215. Thetraining process determines coefficients for the secondary SCISF 300 sothat the output {{circumflex over (x)}_(k)} matches the scaled referencesequence (x*q)_(k) as closely as possible in a least squares sense,i.e., the mean square error between the output and the referencesequence is minimized. Periodically, the coefficients of the secondarySCISF 300 are copied to the primary SCISF 90.

Alternatively, as shown in FIG. 6B, the periodic training may beperformed with a single SCISF 90. In this configuration, a receivedsequence {y_(k)} is output by the A/D 80 in the receiver. The SCISF 90filters and transforms the received sequence {y_(k)} into an outputsequence {{circumflex over (x)}′_(k)}. The received sequence {y_(k)} isalso input to a delay. After the received sequence {y_(k)} passesthrough the SCISF 90, a data switch 360 is changed from position A toposition B; allowing the delayed received sequence to make a second passthrough the SCISF 90. An output switch 370 also may be opened, so thatdata is not output during the training process. In addition, the SCISFcoefficients are controlled by the LMS algorithm during the trainingprocess.

A reference sequence is computed as in the configuration of FIG. 6A. Thedata output of the decoder 140 is input to an encoder 320. The resultingfrequency domain signal is input to a scaling filter 520 which appliesthe set of frequency domain scaling factors Q_(k) that causes the SCISFto adapt to the desired spectral response, as discussed above. Thescaled signal is input to an inverse discrete Fourier transform 330, aparallel to serial converter 340 and a cyclic prefix adder 350,resulting in a scaled reference sequence (x*q)_(k). The scaled referencesequence is input to the LMS algorithm processor.

The output sequence {{circumflex over (x)}_(k)} of the second passthrough the SCISF 90 is compared (in signal comparator 205) to thereference sequence (x*q)_(k). As noted above, the received sequence{y_(k)} passes through a delay 305 before being input to the SCISF 90for the second pass. The delay 305 compensates for the processing delayin the demodulation/decoding chain and the encoding/modulation chain.The comparison results in an error signal e_(k) that is input to the LMSalgorithm processor 215. The training process determines coefficientsfor the SCISF 90 so that the output {{circumflex over (x)}_(k)} matchesthe scaled reference sequence (x*q)_(k) as closely as possible in aleast squares sense, i.e., the mean square error between the output andthe reference sequence is minimized. The coefficients of the SCISF 90then are updated to the coefficients determined in the training process.

In a third embodiment, the system dynamically selects the length of thecyclic prefix (CP) to maximize data throughput for a communicationchannel having a particular noise profile. As discussed above, a CP isadded to each symbol prior to transmission through the communicationchannel to reduce the effects of ISI. However, because the CPconstitutes redundant data, increasing the length of the CP reduces theefficiency of the communication system. Hence, to maximize efficiency,the length of the CP must be as short as the noise characteristics ofthe communication channel permit.

For a DMT communication system with M tones, the maximum sample rate W(samples/second) for a particular channel depends, in part, on theavailable bandwidth and hardware limitations. The sample rate includescommunication data and CP bits. For a CP length of n_(c), the maximumsymbol rate (which includes communication data, but not the CP) isW/(2M+n_(c)).

Before determining the optimal CP length, the SCISF should be initiallytrained to the channel. However, a communication system need not have aSCISF to employ the CP optimization algorithm. It is noted that theSCISF coefficients determined during the training process do not dependon the CP length. The capacity of the sub-channel may be approximated aslog(1+SNR_(i)) bits per second, so the number of bits per symbol isΣ_(i) log(1+SNR_(i)). For a CP length of n_(c), the maximum bit rate isexpressed as a function of the cyclic prefix as:

$\begin{matrix}{{B_{a}\left( n_{c} \right)} = \frac{W{\sum\limits_{i}{\log\left( {1 + {SNR}_{i}} \right)}}}{{2M} + n_{c}}} & (17)\end{matrix}$The optimal CP length is determined by computing the maximum bit ratefor a set of candidate values of CP length and finding the length thatmaximizes B_(a)(n_(c)).

The signal to noise ratio SNR_(i) of each subchannel is determined bymeasuring the received signal and noise power and computing the ratio ofthe two. The noise power γ_(i) for the i^(th) bin may be measured bytransmitting a data communication sequence and computing the average ofthe squares of the errors measured at the output of the receiver DFT.The total received power (signal and noise) δ_(i) for the i^(th) bin maybe measured by computing the average of the squares of the outputs ofthe receiver DFT. The signal to noise ratio is determined from theexpression: δ_(i)/γ_(i)=1+SNR_(i). Since the signal to noise ratio isdetermined in the receiver, the computed bit rate B_(a)(n_(c)) must betransmitted back to the transmitter. The transmitter compares the bitrate to the values computed for other candidate CP lengths and selectsthe CP length n_(c) with the highest maximum bit rate B_(a)(n_(c)).

FIGS. 7A-7D and 8A-8D show performance simulations for test systemsbased on system parameters and test loops described in VDSL AllianceSDMT VDSL Draft Standard Proposal, Technical report, ANSI, 1998; andVery-high-speed digital subscriber lines: System requirements,T1E1.4/97-131R1, Technical report, ANSI, 1997. The results are for aVDSL system working over test loops 2 and 6 of length 4500 feet in theupstream direction. The system has a sampling frequency of 11.04 MHz.Noise is generated by near-end cross talk from an interfering ADSL andan interfering HDSL and white noise at a level of −140 dBm. The SCISFused in the simulations is length −15 FIR. A version of the NormalizedLMS algorithm is used to train the SCISF during an initial trainingperiod using a predetermined transmitted sequence.

FIGS. 7A-7D show the simulated system performance for a communicationsystem having the parameters defined for Test Loop 2, which is 4500 feetin length. FIG. 7A shows channel frequency response with and without aSCISF. The SCISF provides a much more uniform frequency response acrossthe frequency band of interest and significantly improves the signal tonoise ratio (SNR) in the higher frequency bins. FIG. 7B is a plot of theerror signal (10 log|{circumflex over (x)}_(k)−x_(k)|) during thetraining process. The error decreases rapidly during the first fewiterations and is nearly converged after only 20-30 iterations. FIG. 7Cis a plot of transmitted power spectral density, received power spectraldensity and the additive noise power spectral density over the usedsubchannels at the output of the receiver A/D. FIG. 7D is a plot of SNRat the input to the receiver A/D, which is the maximum attainable SNR.The plot also shows the SNR at the output of the receiver DFT without aSCISF and the SNR at the outputs of the receiver DFT using an adaptedSCISF.

FIGS. 8A-8D show the simulated system performance for a communicationsystem having the parameters defined for Test Loop 6, which is 4500 feetin length. FIG. 8A shows channel frequency response with and without aSCISF. FIG. 8B is a plot of the error signal (10 log|{circumflex over(x)}_(k)−x_(k)|) during the training process. FIG. 8C is a plot oftransmitted power spectral density, received power spectral density andthe additive noise power spectral density over the used subchannels atthe output of the receiver AID. FIG. 8D is a plot of SNR at the input tothe receiver A/D. The plot also shows the SNR at the output of thereceiver DFT without a SCISF and the SNR at the outputs of the receiverDFT using an adapted SCISF.

Other embodiments are within the scope of the following claims.

1. A method for transmitting information comprising: selecting a cyclicprefix length from a plurality of candidate lengths based on respectivebit rates obtained for the candidate lengths; and adding an end-portionof a block of information bits at a beginning of the block, wherein theadded end-block portion has a length equal to the selected cyclic prefixlength.
 2. The method of claim 1 including transmitting the block ofinformation bits with the end-portion added thereto through acommunication channel.
 3. The method of claim 1 wherein selecting acyclic prefix length includes: computing a respective maximum bit ratevalue for each of the candidate lengths; and identifying a particularone of the candidate lengths having the largest maximum bit rate valueof the computed maximum bit rate values.
 4. The method of claim 1including: transmitting the computed respective bit rates; andtransmitting the block of information bits with the end-portion addedthereto.
 5. The method of claim 1 wherein selecting comprisesdetermining the signal to noise ratio associated with each of theplurality of candidate lengths.
 6. The method of claim 3 comprising:transmitting the largest maximum bit rate value.
 7. A method ofdynamically selecting a cyclic prefix length, the method comprising:computing a respective maximum bit rate value for each of a plurality ofcandidate cyclic prefix lengths; identifying a particular one of thecandidate cyclic prefix lengths having the largest maximum bit ratevalue of the computed maximum bit rate values; and adding an end-portionof a block of information bits at a beginning of the block, wherein theadded end-block portion has a length equal to the particular onecandidate cyclic prefix length.
 8. The method of claim 7, wherein thecandidate cyclic prefix lengths include at least a first length and asecond length, the method including: transmitting data having a cyclicprefix of the first length; computing a first maximum bit rate value forthe cyclic prefix of the first length; transmitting data having a cyclicprefix of the second length; and computing a second maximum bit ratevalue for the cyclic prefix of the second length.
 9. The method of claim7 wherein computing a respective maximum bit rate value comprisesdetermining the signal to noise ratio associated with each of theplurality of candidate cyclic prefix lengths.
 10. The method of claim 7comprising: transmitting the largest maximum bit rate value.
 11. Themethod of claim 7 wherein: the computing a respective maximum bit ratevalue is performed by a discrete multi-tone receiver; and theidentifying a particular one of the candidate cyclic prefix lengths isperformed by a discrete multi-tone transmitter.
 12. A discretemulti-tone communication system comprising: a discrete multi-tonereceiver comprising: means for computing a bit rate value for each of aplurality of candidate cyclic prefix lengths; means for transmitting thebit rate values; a discrete multi-tone transmitter comprising: means forreceiving the bit rate values; means for identifying a particular one ofthe candidate cyclic prefix lengths having the largest bit rate value ofthe computed bit rate values.
 13. The system of claim 12 wherein thediscrete multi-tone transmitter comprises: means for adding anend-portion of a block of information bits at a beginning of the block,wherein the added end-block portion has a length equal to the particularone candidate cyclic prefix length.
 14. The system of claim 12 whereinthe means for computing a bit rate value determines the signal to noiseratio associated with each of the plurality of candidate cyclic prefixlengths.
 15. An article comprising a machine-readable medium that storesmachine-executable instructions for causing a machine to: select acyclic prefix length from a plurality of candidate lengths based onrespective bit rates obtained for the candidate lengths; and add anend-portion of a block of information bits at a beginning of the block,wherein the added end-block portion has a length equal to the selectedcyclic prefix length.
 16. The article of claim 15, further causing amachine to: transmit the block of information bits with the end-portionadded thereto through a communication channel.
 17. The article of claim15, further causing a machine to: compute a respective maximum bit ratevalue for each of the candidate lengths; and identify a particular oneof the candidate lengths having the largest maximum bit rate value ofthe computed maximum bit rate values.
 18. The article of claim 15,further causing a machine to: transmit the computed respective bitrates; and transmit the block of information bits with the end-portionadded thereto.
 19. The article of claim 15, further causing a machineto: determine the signal to noise ratio associated with each of theplurality of candidate lengths.
 20. An article comprising amachine-readable medium that stores machine-executable instructions forcausing a machine to: compute a respective maximum bit rate value foreach of a plurality of candidate cyclic prefix lengths; identify aparticular one of the candidate cyclic prefix lengths having the largestmaximum bit rate value of the computed maximum bit rate values; and addan end-portion of a block of information bits at a beginning of theblock, wherein the added end-block portion has a length equal to theparticular one candidate cyclic prefix length.
 21. The article of claim20, further causing a machine to: transmit the largest maximum bit ratevalue.
 22. The article of claim 20, further causing a machine to:determine the signal to noise ratio associated with each of theplurality of candidate cyclic prefix lengths.